Average Error: 18.4 → 13.3
Time: 11.1s
Precision: 64
Internal Precision: 576
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -2.8626604681224874 \cdot 10^{-93}:\\ \;\;\;\;\left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot c0\right) \cdot \sqrt{\sqrt{\frac{1}{\frac{V \cdot \ell}{A}}}}\\ \mathbf{elif}\;V \cdot \ell \le 6.918776883571572 \cdot 10^{-263} \lor \neg \left(V \cdot \ell \le 4.1943447453160254 \cdot 10^{+290}\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A} \cdot c0}{\sqrt{V \cdot \ell}}\\ \end{array}\]

Error

Bits error versus c0

Bits error versus A

Bits error versus V

Bits error versus l

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if (* V l) < -2.8626604681224874e-93

    1. Initial program 13.6

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
    2. Using strategy rm

    3. Applied add-sqr-sqrt13.6

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\sqrt{\frac{A}{V \cdot \ell}} \cdot \sqrt{\frac{A}{V \cdot \ell}}}}\]

    4. Applied sqrt-prod13.8

      \[\leadsto c0 \cdot \color{blue}{\left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right)}\]

    5. Applied associate-*r*13.8

      \[\leadsto \color{blue}{\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}}\]
    6. Using strategy rm

    7. Applied clear-num14.1

      \[\leadsto \left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right) \cdot \sqrt{\sqrt{\color{blue}{\frac{1}{\frac{V \cdot \ell}{A}}}}}\]

    if -2.8626604681224874e-93 < (* V l) < 6.918776883571572e-263 or 4.1943447453160254e+290 < (* V l)

    1. Initial program 34.8

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
    2. Using strategy rm

    3. Applied div-inv35.5

      \[\leadsto c0 \cdot \sqrt{\color{blue}{A \cdot \frac{1}{V \cdot \ell}}}\]
    4. Using strategy rm

    5. Applied *-un-lft-identity35.5

      \[\leadsto c0 \cdot \color{blue}{\left(1 \cdot \sqrt{A \cdot \frac{1}{V \cdot \ell}}\right)}\]

    6. Applied associate-*r*35.5

      \[\leadsto \color{blue}{\left(c0 \cdot 1\right) \cdot \sqrt{A \cdot \frac{1}{V \cdot \ell}}}\]

    7. Simplified25.8

      \[\leadsto \left(c0 \cdot 1\right) \cdot \color{blue}{\sqrt{\frac{\frac{A}{\ell}}{V}}}\]

    if 6.918776883571572e-263 < (* V l) < 4.1943447453160254e+290

    1. Initial program 9.6

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
    2. Using strategy rm

    3. Applied sqrt-div0.4

      \[\leadsto c0 \cdot \color{blue}{\frac{\sqrt{A}}{\sqrt{V \cdot \ell}}}\]

    4. Applied associate-*r/2.4

      \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification13.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -2.8626604681224874 \cdot 10^{-93}:\\ \;\;\;\;\left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot c0\right) \cdot \sqrt{\sqrt{\frac{1}{\frac{V \cdot \ell}{A}}}}\\ \mathbf{elif}\;V \cdot \ell \le 6.918776883571572 \cdot 10^{-263} \lor \neg \left(V \cdot \ell \le 4.1943447453160254 \cdot 10^{+290}\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{A} \cdot c0}{\sqrt{V \cdot \ell}}\\ \end{array}\]

Runtime

Time bar (total: 11.1s)Debug logProfile

herbie shell --seed 2018219 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))